Odd sized showerhead connector

Please forgive my lack of knowledge on proper terminology, but even with searching google images I couldn't find the correct names, lol ;->.... things I didnt' know are followed by "(?)"....

At any rate, what I've come across in a new rental is an outdoor shower whose showerhead leaks profusely--has cracks and such, and needs replaced. I purchased a new showerhead and it doesn't fit! The female end that screws onto the wall outlet elbow (?) is substantially bigger than on standard showerheads, oddly. It (and the wall outlet elbow) seems to be the same size as a garden hose spigot, but I can't seem to find any reference anywhere to showerheads that have non standard sized connectors (?), let alone where I'd find a showerhead that fits on something that size. Very confused!

we have absolutely no idea what you are describing. ANY new shower head should have the conventional 1/2" ips size, unless you are removing the "ball joint" and trying to attach the head directly to something.